On the Domination Conditions for Families of Quasinearly Subharmonic Functions

Abstract

Domar has given a condition that ensures the existence of the largest subharmonic minorant of a given function. Later Rippon pointed out that a modification of Domars argument gives in fact a better result. Using our previous, rather general and flexible modifications of Domars original argument, we extend their results both to the subharmonic and to the quasinearly subharmonic settings.